Bahrain's King Hamad Bin Isa Al-Khalifa, Qatari Emir Sheikh Tamim Bin Hamad Al-Thani, a high-level delegation from the United Arab Emirates and Kuwait's Emir Sheikh Sabah Al-Ahmad Al-Sabah were at the funeral, state television showed on Friday.

King Salman, 79, in his first public address, pledged no change in the kingdom's direction and called for unity among Muslims.

"We will remain with God's strength attached to the straight path that this state has walked since its establishment by King Abdul Aziz bin al-Saud, and by his sons after him," Salman said his in televised remarks.

Prince Muqrin Bin Abdulaziz has been announced as the new crown prince, state TV announced.

The new king also appointed his nephew Mohammed bin Nayef as deputy crown prince, meaning he will be the first person of the next generation to rule the kingdom one day.

Prince Mohammed, who remains as interior minister, according to the royal decree carried on state television, is next in line to rule after Salman and Crown Prince Muqrin.

Obama condolences

US President Barack Obama offered his condolences on King Abdullah's death.

"As our countries worked together to confront many challenges, I always valued King Abdullah's perspective and appreciated our genuine and warm friendship," Obama said in a written statement.

"The closeness and strength of the partnership between our two countries is part of King Abdullah's legacy."

King Abdullah, thought to have been born in 1923, took the throne in 2005, but had run the country as de facto regent for a decade before that after his predecessor King Fahd suffered a debilitating stroke.

At stake with the appointment of Salman as king is the future direction of the US' most important Arab ally and self-appointed champion of Sunni Islam at a moment of unprecedented turmoil across the Middle East.

Most recently, the kingdom joined the US-led coalition carrying out air strikes against the Islamic State of Iraq and the Levant.

King Abdullah played a guiding role in Saudi Arabia's support for Egypt's government after the military intervened in 2013, and drove his country's support for Syria's rebellion against President Bashar al-Assad.

King Salman has been crown prince since 2012 and has been heading the defence ministry since 2011. He was governor of Riyadh province for five decades before that.